Algorithms for Geometric Computational Problems Considering Constraints from Practice and Their Applications

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In this research we have dealt with the following three problems on computational geometry from a unified point of view. For the first problem we have developed a memory-efficient algorithm for mapping objects in a low-dimensional space so that their dissimilarity is reflected as their distance. For the second problem on triangular mesh we have developed an algorithm based on practical criteria. The third problem is on trisector curves for two points in the plane. We have proved many mathematical properties on the curve together with efficient algorithms for drawing.